Block #1,973,674

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/7/2017, 10:15:58 PM · Difficulty 10.7547 · 4,868,821 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4baa63e430b89e3bc14fbcde32405f0e89558edb3a6601e7442018246e21a12

View on Chainz ↗

Height

#1,973,674

Difficulty

10.754707

Transactions

Size

870 B

Version

Bits

0ac1347a

Nonce

350,068,697

Timestamp

2/7/2017, 10:15:58 PM

Confirmations

4,868,821

Mined by

⛏️ P2SHAGFhJEprSosRRa1MAhAtqykA8E1uZFJeTy

Merkle Root

a634f3b045e92929d858c066de17423d77d7e33b7783b0aa645cc0946875573c

Transactions (2)

Coinbase8004a994c3edca…929929c968578d

1 in → 1 out8.6400 XPM109 B

AGFhJEpr…1uZFJeTy

910a311f2e7b9a…298a5fb55a4115

4 in → 2 out1493.0556 XPM670 B

AGBaEwwH…pt2Jow2q AZ7xo3ni…aXTAFhZR

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.

1.176 × 10⁹⁷(98-digit number)

11768897964518459781…41727753421361305599

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

1.176 × 10⁹⁷(98-digit number)

11768897964518459781…41727753421361305599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.176 × 10⁹⁷(98-digit number)

11768897964518459781…41727753421361305601

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

2.353 × 10⁹⁷(98-digit number)

23537795929036919562…83455506842722611199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.353 × 10⁹⁷(98-digit number)

23537795929036919562…83455506842722611201

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

4.707 × 10⁹⁷(98-digit number)

47075591858073839125…66911013685445222399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.707 × 10⁹⁷(98-digit number)

47075591858073839125…66911013685445222401

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

9.415 × 10⁹⁷(98-digit number)

94151183716147678251…33822027370890444799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.415 × 10⁹⁷(98-digit number)

94151183716147678251…33822027370890444801

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

1.883 × 10⁹⁸(99-digit number)

18830236743229535650…67644054741780889599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.883 × 10⁹⁸(99-digit number)

18830236743229535650…67644054741780889601

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,973,674

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