Block #880,161

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2015, 5:44:15 AM · Difficulty 10.9620 · 5,937,611 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40b9c15c801f3444ae2ba265c2b960c4bc0fc6580095a5d87d385fa8b8e8269f

View on Chainz ↗

Height

#880,161

Difficulty

10.962025

Transactions

Size

1.01 KB

Version

Bits

0af6474d

Nonce

350,571,112

Timestamp

1/3/2015, 5:44:15 AM

Confirmations

5,937,611

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

46117b5650f66147073a72008ea49fee88e62c42d6d02119f0169ee289607e27

Transactions (4)

Coinbasee82b1f28e91918…4b0d60a7d110a8

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

3b4acd860ddfad…ea69da82ee68bf

1 in → 2 out5.4988 XPM226 B

AZcjuYFn…X2P5T1gC AKZMVBtp…Lh7ZP1EZ

5211f72fe47329…1afa64468f54b2

1 in → 2 out2.7043 XPM226 B

APnh1EC7…jLd3BXjj AVBdRQoA…MW5KYkB4

24814b2210ff76…1e47a7d99e5663

2 in → 2 out5.1971 XPM372 B

AN7LXk1L…ciED84V4 AYrwBKyU…1S6w2wRP

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.

1.037 × 10⁹⁶(97-digit number)

10372133102908665754…73768558102914080639

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

1.037 × 10⁹⁶(97-digit number)

10372133102908665754…73768558102914080639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.037 × 10⁹⁶(97-digit number)

10372133102908665754…73768558102914080641

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

2.074 × 10⁹⁶(97-digit number)

20744266205817331508…47537116205828161279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.074 × 10⁹⁶(97-digit number)

20744266205817331508…47537116205828161281

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

4.148 × 10⁹⁶(97-digit number)

41488532411634663016…95074232411656322559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.148 × 10⁹⁶(97-digit number)

41488532411634663016…95074232411656322561

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

8.297 × 10⁹⁶(97-digit number)

82977064823269326032…90148464823312645119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.297 × 10⁹⁶(97-digit number)

82977064823269326032…90148464823312645121

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

1.659 × 10⁹⁷(98-digit number)

16595412964653865206…80296929646625290239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.659 × 10⁹⁷(98-digit number)

16595412964653865206…80296929646625290241

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 #880,161

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