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Block #2,833,139

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 1:16:32 PM Β· Difficulty 11.7150 Β· 4,006,994 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4ddfc1ba72ce562f533498fd901638efa97c58bffd0fb77a06d1e4787485ed7d
View on Chainz β†—

Height

#2,833,139

Difficulty

11.715011

Transactions

1

Size

200 B

Version

2

Bits

0bb70af7

Nonce

592,345,817

Timestamp

9/10/2018, 1:16:32 PM

Confirmations

4,006,994

Mined by

⛏️ P2SHAGvn5PUXPqEiW4DRb6F8VkpfzW42zVXyYP

Merkle Root

2321187de38a24f6bea4681ad5ee1d4adb1c1be484fcfa5ed914c10f740011f5
Transactions (1)
Coinbase2321187de38a24…14c10f740011f5
1 in β†’ 1 out7.2700 XPM109 B
AGvn5PUX…42zVXyYP
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.

1.417 Γ— 10⁹⁷(98-digit number)
14174342091696319092…22673728518668766719
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
1.417 Γ— 10⁹⁷(98-digit number)
14174342091696319092…22673728518668766719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.417 Γ— 10⁹⁷(98-digit number)
14174342091696319092…22673728518668766721
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
2.834 Γ— 10⁹⁷(98-digit number)
28348684183392638184…45347457037337533439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.834 Γ— 10⁹⁷(98-digit number)
28348684183392638184…45347457037337533441
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
5.669 Γ— 10⁹⁷(98-digit number)
56697368366785276368…90694914074675066879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.669 Γ— 10⁹⁷(98-digit number)
56697368366785276368…90694914074675066881
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
1.133 Γ— 10⁹⁸(99-digit number)
11339473673357055273…81389828149350133759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.133 Γ— 10⁹⁸(99-digit number)
11339473673357055273…81389828149350133761
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
2.267 Γ— 10⁹⁸(99-digit number)
22678947346714110547…62779656298700267519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.267 Γ— 10⁹⁸(99-digit number)
22678947346714110547…62779656298700267521
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
4.535 Γ— 10⁹⁸(99-digit number)
45357894693428221094…25559312597400535039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,965,379 XPMΒ·at block #6,840,132 Β· updates every 60s
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