Block #2,652,868

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/7/2018, 11:00:21 PM · Difficulty 11.7414 · 4,184,213 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f98349e5eb34f7600caca04eb62773e5790fdfeb4a9655b72bf56945dee5c649

View on Chainz ↗

Height

#2,652,868

Difficulty

11.741372

Transactions

Size

880 B

Version

Bits

0bbdca87

Nonce

464,280,819

Timestamp

5/7/2018, 11:00:21 PM

Confirmations

4,184,213

Mined by

⛏️ P2SHAdbCxkQtKqEEF1WjN8ZoAPW3Cvg6NyQW8Y

Merkle Root

89e9a622abe448f28eb11d1544de6b4dfef3032bc999bde026b12e8684c6d078

Transactions (3)

Coinbasee194954e6e86f7…32acd2b05c0892

1 in → 1 out7.2600 XPM110 B

AdbCxkQt…g6NyQW8Y

33fea94cf5d552…4d7b11e96f78da

2 in → 2 out14.4200 XPM305 B

AXSM1qLg…y1Yfkh2S AW98TjP4…Aw1T7wA9

992bbc4efb5189…fff4a985e89e46

2 in → 2 out0.6480 XPM373 B

AG9R5hSw…wd4pNJH3 AFsam1cP…BcLTBxZU

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.

3.649 × 10⁹⁸(99-digit number)

36495015807592311163…53266510192372613119

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

3.649 × 10⁹⁸(99-digit number)

36495015807592311163…53266510192372613119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.649 × 10⁹⁸(99-digit number)

36495015807592311163…53266510192372613121

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

7.299 × 10⁹⁸(99-digit number)

72990031615184622326…06533020384745226239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.299 × 10⁹⁸(99-digit number)

72990031615184622326…06533020384745226241

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

1.459 × 10⁹⁹(100-digit number)

14598006323036924465…13066040769490452479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.459 × 10⁹⁹(100-digit number)

14598006323036924465…13066040769490452481

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

2.919 × 10⁹⁹(100-digit number)

29196012646073848930…26132081538980904959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.919 × 10⁹⁹(100-digit number)

29196012646073848930…26132081538980904961

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

5.839 × 10⁹⁹(100-digit number)

58392025292147697860…52264163077961809919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.839 × 10⁹⁹(100-digit number)

58392025292147697860…52264163077961809921

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

1.167 × 10¹⁰⁰(101-digit number)

11678405058429539572…04528326155923619839

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.167 × 10¹⁰⁰(101-digit number)

11678405058429539572…04528326155923619841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,652,868

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