Block #851,337

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2014, 5:36:28 AM · Difficulty 10.9707 · 5,959,734 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

80811fa7523f9b37415f461feca894d31eb885bbde0658d455a569f77d3bbcde

View on Chainz ↗

Height

#851,337

Difficulty

10.970651

Transactions

Size

432 B

Version

Bits

0af87c9a

Nonce

155,697,701

Timestamp

12/13/2014, 5:36:28 AM

Confirmations

5,959,734

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4597ff32bd9a472434824994e4983aa9173e2a1da83bf761ae95273b0b6b2437

Transactions (2)

Coinbase2e3df92c9a51ad…197187b4767ce7

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

aa849844db6d61…655cc69204f1e3

1 in → 2 out4.8766 XPM226 B

ARhpUtWr…EkbGV51F AU3EgHPb…DCRaDoTM

Prime Chain Origin

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

9.408 × 10⁹⁴(95-digit number)

94082401784378692292…16221511573220646009

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

9.408 × 10⁹⁴(95-digit number)

94082401784378692292…16221511573220646009

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.408 × 10⁹⁴(95-digit number)

94082401784378692292…16221511573220646011

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.881 × 10⁹⁵(96-digit number)

18816480356875738458…32443023146441292019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.881 × 10⁹⁵(96-digit number)

18816480356875738458…32443023146441292021

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.763 × 10⁹⁵(96-digit number)

37632960713751476916…64886046292882584039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.763 × 10⁹⁵(96-digit number)

37632960713751476916…64886046292882584041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.526 × 10⁹⁵(96-digit number)

75265921427502953833…29772092585765168079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.526 × 10⁹⁵(96-digit number)

75265921427502953833…29772092585765168081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.505 × 10⁹⁶(97-digit number)

15053184285500590766…59544185171530336159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.505 × 10⁹⁶(97-digit number)

15053184285500590766…59544185171530336161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #851,337

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