Block #658,069

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/1/2014, 4:05:18 PM · Difficulty 10.9562 · 6,148,176 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92c1f3ecaccbac66747b5a35c457c5a48abb100ede92cf86ea430247d0c49be4

View on Chainz ↗

Height

#658,069

Difficulty

10.956248

Transactions

Size

1.70 KB

Version

Bits

0af4ccb3

Nonce

586,169,450

Timestamp

8/1/2014, 4:05:18 PM

Confirmations

6,148,176

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e34594c834e03ee02db845ea93cee6055833fe10532280ab614ed3f3a7eca1ee

Transactions (5)

Coinbaseeccce2e5c051df…a4baa7f2dc7bc8

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

e546e7cf081869…28e4ed6b560a29

4 in → 2 out20.8903 XPM669 B

AUyTyEwu…Lu5tSJFg AaU9J1Lk…4e47uLfq

e73d78544e4d53…d5d4792ccac3e8

2 in → 2 out11.5356 XPM376 B

AZpeGnSF…4cbyDNBL ASriUFM6…RyQM3vvk

8aed1a9ec9cdba…264a9dd9566d2e

1 in → 3 out4.2288 XPM261 B

AeKNrjNj…1NEq95Ta AL5wNHbW…dFU2npvz AZa2QvH4…JvH9i3cj

d4b81d395bbe79…9a435b21a91124

1 in → 2 out1.1298 XPM227 B

AToctXWm…mgEtBv9N AbWPoHBn…7bMc9VTV

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.

1.314 × 10⁹⁶(97-digit number)

13141868933645820377…48080138825616424959

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

1.314 × 10⁹⁶(97-digit number)

13141868933645820377…48080138825616424959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.314 × 10⁹⁶(97-digit number)

13141868933645820377…48080138825616424961

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

2.628 × 10⁹⁶(97-digit number)

26283737867291640754…96160277651232849919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.628 × 10⁹⁶(97-digit number)

26283737867291640754…96160277651232849921

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

5.256 × 10⁹⁶(97-digit number)

52567475734583281509…92320555302465699839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.256 × 10⁹⁶(97-digit number)

52567475734583281509…92320555302465699841

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

1.051 × 10⁹⁷(98-digit number)

10513495146916656301…84641110604931399679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.051 × 10⁹⁷(98-digit number)

10513495146916656301…84641110604931399681

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

2.102 × 10⁹⁷(98-digit number)

21026990293833312603…69282221209862799359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.102 × 10⁹⁷(98-digit number)

21026990293833312603…69282221209862799361

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

4.205 × 10⁹⁷(98-digit number)

42053980587666625207…38564442419725598719

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 #658,069

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