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Block #2,644,626

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 2:04:44 PM Β· Difficulty 11.7137 Β· 4,198,163 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c9f947cd03a1e7f5074337907fe4cce69c56d8682a815f50fca8b87d73aa3110
View on Chainz β†—

Height

#2,644,626

Difficulty

11.713717

Transactions

1

Size

200 B

Version

2

Bits

0bb6b625

Nonce

1,304,510,041

Timestamp

5/2/2018, 2:04:44 PM

Confirmations

4,198,163

Mined by

⛏️ P2SHAbZqQcYC8mL4MsZbojMY4RNfjXa5ktWtZV

Merkle Root

a36fdc9a6bf84d855ee99002ab766ba930641e2b9b944296e721a95c3d384f23
Transactions (1)
Coinbasea36fdc9a6bf84d…21a95c3d384f23
1 in β†’ 1 out7.2800 XPM110 B
AbZqQcYC…a5ktWtZV
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.

6.580 Γ— 10⁹⁴(95-digit number)
65806864866500122717…00864609061520488319
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
6.580 Γ— 10⁹⁴(95-digit number)
65806864866500122717…00864609061520488319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.580 Γ— 10⁹⁴(95-digit number)
65806864866500122717…00864609061520488321
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
1.316 Γ— 10⁹⁡(96-digit number)
13161372973300024543…01729218123040976639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.316 Γ— 10⁹⁡(96-digit number)
13161372973300024543…01729218123040976641
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
2.632 Γ— 10⁹⁡(96-digit number)
26322745946600049086…03458436246081953279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.632 Γ— 10⁹⁡(96-digit number)
26322745946600049086…03458436246081953281
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
5.264 Γ— 10⁹⁡(96-digit number)
52645491893200098173…06916872492163906559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.264 Γ— 10⁹⁡(96-digit number)
52645491893200098173…06916872492163906561
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
1.052 Γ— 10⁹⁢(97-digit number)
10529098378640019634…13833744984327813119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.052 Γ— 10⁹⁢(97-digit number)
10529098378640019634…13833744984327813121
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
2.105 Γ— 10⁹⁢(97-digit number)
21058196757280039269…27667489968655626239
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:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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