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Block #1,371,821

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 6:42:26 PM Β· Difficulty 10.8102 Β· 5,468,827 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
72e2cab55c8740856cf8da19c3f54d716cf86940bf3236ce000d5b0e775f7396
View on Chainz β†—

Height

#1,371,821

Difficulty

10.810203

Transactions

1

Size

200 B

Version

2

Bits

0acf6974

Nonce

728,446,247

Timestamp

12/16/2015, 6:42:26 PM

Confirmations

5,468,827

Mined by

⛏️ P2SHANBm8zfD5eozDxEGZzCjMGtxEL4W7DchSL

Merkle Root

cb0dcb14331e28af269f0719ded514ce0bfb1537525ab0af199a5034de07df83
Transactions (1)
Coinbasecb0dcb14331e28…9a5034de07df83
1 in β†’ 1 out8.5400 XPM109 B
ANBm8zfD…4W7DchSL
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.

1.671 Γ— 10⁹⁢(97-digit number)
16718069297949415496…64485865747179069439
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
1.671 Γ— 10⁹⁢(97-digit number)
16718069297949415496…64485865747179069439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.671 Γ— 10⁹⁢(97-digit number)
16718069297949415496…64485865747179069441
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
3.343 Γ— 10⁹⁢(97-digit number)
33436138595898830993…28971731494358138879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.343 Γ— 10⁹⁢(97-digit number)
33436138595898830993…28971731494358138881
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
6.687 Γ— 10⁹⁢(97-digit number)
66872277191797661987…57943462988716277759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.687 Γ— 10⁹⁢(97-digit number)
66872277191797661987…57943462988716277761
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
1.337 Γ— 10⁹⁷(98-digit number)
13374455438359532397…15886925977432555519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.337 Γ— 10⁹⁷(98-digit number)
13374455438359532397…15886925977432555521
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
2.674 Γ— 10⁹⁷(98-digit number)
26748910876719064795…31773851954865111039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.674 Γ— 10⁹⁷(98-digit number)
26748910876719064795…31773851954865111041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,969,526 XPMΒ·at block #6,840,647 Β· updates every 60s
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