Block #2,949,700

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/3/2018, 3:51:04 AM · Difficulty 11.3969 · 3,893,205 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

39d843137b156106bf05c5c16b40c61e562b83137db0ac4ed4c6cc9a0fd7e5a6

View on Chainz ↗

Height

#2,949,700

Difficulty

11.396880

Transactions

Size

879 B

Version

Bits

0b6599ec

Nonce

226,939,729

Timestamp

12/3/2018, 3:51:04 AM

Confirmations

3,893,205

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

cc3fed485141c36881bf2052057779e39146ed2acc7cb7b427bbb6f9a280a5af

Transactions (3)

Coinbase76734e3d0dfece…615354d4f0abec

1 in → 1 out7.7100 XPM110 B

AbXwmGxD…4XXYP765

78d53504a057fa…5b716c77a7e8ea

2 in → 2 out11.3503 XPM338 B

AbXwmGxD…4XXYP765 AVeV4S3e…YngoJzRw

7cedf0734f77bd…6020fb6cb6d70e

2 in → 2 out10.1743 XPM339 B

ARKFud7A…JRaX29qB AbXwmGxD…4XXYP765

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.

1.482 × 10¹⁰⁰(101-digit number)

14824704662204646191…96762340180597145599

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

1.482 × 10¹⁰⁰(101-digit number)

14824704662204646191…96762340180597145599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.482 × 10¹⁰⁰(101-digit number)

14824704662204646191…96762340180597145601

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

2.964 × 10¹⁰⁰(101-digit number)

29649409324409292382…93524680361194291199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.964 × 10¹⁰⁰(101-digit number)

29649409324409292382…93524680361194291201

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

5.929 × 10¹⁰⁰(101-digit number)

59298818648818584764…87049360722388582399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.929 × 10¹⁰⁰(101-digit number)

59298818648818584764…87049360722388582401

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

1.185 × 10¹⁰¹(102-digit number)

11859763729763716952…74098721444777164799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.185 × 10¹⁰¹(102-digit number)

11859763729763716952…74098721444777164801

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

2.371 × 10¹⁰¹(102-digit number)

23719527459527433905…48197442889554329599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.371 × 10¹⁰¹(102-digit number)

23719527459527433905…48197442889554329601

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

4.743 × 10¹⁰¹(102-digit number)

47439054919054867811…96394885779108659199

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 #2,949,700

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