Block #124,661

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/19/2013, 6:53:03 PM · Difficulty 9.7724 · 6,691,386 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed8c075a13964a217ea15babb75f5b9c22db0bbcb29408603dea1a514946b6f9

View on Chainz ↗

Height

#124,661

Difficulty

9.772394

Transactions

Size

651 B

Version

Bits

09c5bba1

Nonce

250,813

Timestamp

8/19/2013, 6:53:03 PM

Confirmations

6,691,386

Mined by

⛏️ P2SHAY88KHSTJpyaPqTYGEt3LWdPpt88L8yacq

Merkle Root

0470d469a5b3cf3dc7fd8b655c4962d199f6596a04fa72c63a36de272c7b8ed2

Transactions (3)

Coinbasecda523050b26a0…617fc71f80e2de

1 in → 1 out10.4800 XPM109 B

AY88KHST…88L8yacq

afb823b3eba73f…159bcfe9438061

1 in → 2 out8.3898 XPM225 B

AdPAWqTV…i3y99VBA APwXmRMD…5F7RDjwG

d14a0964417ed5…b6f3e3550eaba7

1 in → 2 out7.4735 XPM225 B

APCkfbuz…qViMrwDj ARujT4Ez…fjHkKN7C

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.

6.849 × 10⁹⁹(100-digit number)

68499263271720783592…72974687629405901669

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

6.849 × 10⁹⁹(100-digit number)

68499263271720783592…72974687629405901669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.849 × 10⁹⁹(100-digit number)

68499263271720783592…72974687629405901671

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

1.369 × 10¹⁰⁰(101-digit number)

13699852654344156718…45949375258811803339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.369 × 10¹⁰⁰(101-digit number)

13699852654344156718…45949375258811803341

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

2.739 × 10¹⁰⁰(101-digit number)

27399705308688313437…91898750517623606679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.739 × 10¹⁰⁰(101-digit number)

27399705308688313437…91898750517623606681

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

5.479 × 10¹⁰⁰(101-digit number)

54799410617376626874…83797501035247213359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.479 × 10¹⁰⁰(101-digit number)

54799410617376626874…83797501035247213361

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

1.095 × 10¹⁰¹(102-digit number)

10959882123475325374…67595002070494426719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #124,661

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