Block #581,259

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/8/2014, 2:18:24 PM · Difficulty 10.9627 · 6,232,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

195f083013bf643aa7cdc55ffa1e2bad9fb98cd1248f6d07af5651aaa0d96d46

View on Chainz ↗

Height

#581,259

Difficulty

10.962689

Transactions

Size

2.10 KB

Version

Bits

0af672cc

Nonce

13,345,513

Timestamp

6/8/2014, 2:18:24 PM

Confirmations

6,232,574

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e04a3fe67727d299edb84cb8c8e5f25567bb8fe64c0ddfaa58931f05a631e6ad

Transactions (5)

Coinbaseadf933b1294541…7208185ca836d2

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

5642f2511bb0d3…cc028ffbbf6728

8 in → 2 out5600.0100 XPM1.23 KB

AZd9MT9j…5jj5HB1f Ae7NTJjC…t5spxXEQ

cf512c36c410f6…4246f75ddc32f0

1 in → 2 out8.2900 XPM226 B

AGdWVjRk…LFVsqCnK AeqgyW6e…y9fmPLVt

3e3481a12b5c7b…933a5c7dede56b

1 in → 2 out6.6115 XPM227 B

AXgdY4Xj…v6f2Wb6j ASfQj9Pb…Q87HBF2g

ceaabc47b2fe48…a4f28e87a0e3e2

1 in → 2 out5.8348 XPM227 B

APJus74o…DpDBApyV AL4RdTaL…RQtoEqnD

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.

2.040 × 10¹⁰⁰(101-digit number)

20405326287835486212…72578205783265157119

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

2.040 × 10¹⁰⁰(101-digit number)

20405326287835486212…72578205783265157119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.040 × 10¹⁰⁰(101-digit number)

20405326287835486212…72578205783265157121

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

4.081 × 10¹⁰⁰(101-digit number)

40810652575670972425…45156411566530314239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.081 × 10¹⁰⁰(101-digit number)

40810652575670972425…45156411566530314241

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

8.162 × 10¹⁰⁰(101-digit number)

81621305151341944850…90312823133060628479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.162 × 10¹⁰⁰(101-digit number)

81621305151341944850…90312823133060628481

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

1.632 × 10¹⁰¹(102-digit number)

16324261030268388970…80625646266121256959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.632 × 10¹⁰¹(102-digit number)

16324261030268388970…80625646266121256961

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

3.264 × 10¹⁰¹(102-digit number)

32648522060536777940…61251292532242513919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.264 × 10¹⁰¹(102-digit number)

32648522060536777940…61251292532242513921

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.529 × 10¹⁰¹(102-digit number)

65297044121073555880…22502585064485027839

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 #581,259

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