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Block #2,802,506

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/20/2018, 6:39:01 PM Β· Difficulty 11.6703 Β· 4,036,314 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
7feef6725e27cbaae6ee0b480e672f2771f6a836e0c7839701f2d25e4736fd6b
View on Chainz β†—

Height

#2,802,506

Difficulty

11.670327

Transactions

1

Size

199 B

Version

2

Bits

0bab9a85

Nonce

2,003,476,823

Timestamp

8/20/2018, 6:39:01 PM

Confirmations

4,036,314

Mined by

⛏️ P2SHANpMbpsNcSRRoUGwbyP88a6dPbLi5LjCLL

Merkle Root

9648244487e9ca416d0e56088fed9c4f33b1d93e4eef472b6a8bd58429233ca7
Transactions (1)
Coinbase9648244487e9ca…8bd58429233ca7
1 in β†’ 1 out7.3300 XPM110 B
ANpMbpsN…Li5LjCLL
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.181 Γ— 10⁹¹(92-digit number)
21813946992560216394…89869871229061853119
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.181 Γ— 10⁹¹(92-digit number)
21813946992560216394…89869871229061853119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.181 Γ— 10⁹¹(92-digit number)
21813946992560216394…89869871229061853121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.362 Γ— 10⁹¹(92-digit number)
43627893985120432788…79739742458123706239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.362 Γ— 10⁹¹(92-digit number)
43627893985120432788…79739742458123706241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
8.725 Γ— 10⁹¹(92-digit number)
87255787970240865576…59479484916247412479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.725 Γ— 10⁹¹(92-digit number)
87255787970240865576…59479484916247412481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.745 Γ— 10⁹²(93-digit number)
17451157594048173115…18958969832494824959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.745 Γ— 10⁹²(93-digit number)
17451157594048173115…18958969832494824961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.490 Γ— 10⁹²(93-digit number)
34902315188096346230…37917939664989649919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.490 Γ— 10⁹²(93-digit number)
34902315188096346230…37917939664989649921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.980 Γ— 10⁹²(93-digit number)
69804630376192692461…75835879329979299839
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
6.980 Γ— 10⁹²(93-digit number)
69804630376192692461…75835879329979299841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,954,825 XPMΒ·at block #6,838,819 Β· updates every 60s
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