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Block #1,036,908

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2015, 12:19:19 AM Β· Difficulty 10.7401 Β· 5,777,311 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
161fc92046104a76458c57fd1c6f6da86ad4f74f4053bc250d6d9e5fc914b6e1
View on Chainz β†—

Height

#1,036,908

Difficulty

10.740143

Transactions

1

Size

199 B

Version

2

Bits

0abd79fe

Nonce

144,665

Timestamp

4/29/2015, 12:19:19 AM

Confirmations

5,777,311

Mined by

⛏️ P2SHAcH2s7Y4D9hVCSQQdA7jo9e2ue1nk8yDe6

Merkle Root

68b5d636b62b92cc7d11c8d5362586917fcc2e4c798955b22c65368476b47ac3
Transactions (1)
Coinbase68b5d636b62b92…65368476b47ac3
1 in β†’ 1 out8.6600 XPM109 B
AcH2s7Y4…1nk8yDe6
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.

1.557 Γ— 10⁹⁡(96-digit number)
15570793096955663249…14928789682930794579
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
1.557 Γ— 10⁹⁡(96-digit number)
15570793096955663249…14928789682930794579
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.557 Γ— 10⁹⁡(96-digit number)
15570793096955663249…14928789682930794581
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
3.114 Γ— 10⁹⁡(96-digit number)
31141586193911326499…29857579365861589159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.114 Γ— 10⁹⁡(96-digit number)
31141586193911326499…29857579365861589161
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
6.228 Γ— 10⁹⁡(96-digit number)
62283172387822652999…59715158731723178319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.228 Γ— 10⁹⁡(96-digit number)
62283172387822652999…59715158731723178321
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
1.245 Γ— 10⁹⁢(97-digit number)
12456634477564530599…19430317463446356639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.245 Γ— 10⁹⁢(97-digit number)
12456634477564530599…19430317463446356641
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
2.491 Γ— 10⁹⁢(97-digit number)
24913268955129061199…38860634926892713279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.491 Γ— 10⁹⁢(97-digit number)
24913268955129061199…38860634926892713281
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:57,757,821 XPMΒ·at block #6,814,218 Β· updates every 60s
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