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Block #604,685

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2014, 11:41:24 PM Β· Difficulty 10.9103 Β· 6,192,192 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dea114e3c80dd789acffd90b8b5ab027779c3287f31a5ae8cdf4170ecde7a84c
View on Chainz β†—

Height

#604,685

Difficulty

10.910260

Transactions

1

Size

188 B

Version

2

Bits

0ae906d2

Nonce

81,957

Timestamp

6/27/2014, 11:41:24 PM

Confirmations

6,192,192

Mined by

AYCeLhqBJ84jFrKumsmd4mf6paeqGM6KK1

Merkle Root

883262b6cca7399ab789373fe17f8dc50b26232e053b5a13f201308671c394e3
Transactions (1)
Coinbase883262b6cca739…01308671c394e3
1 in β†’ 1 out8.3900 XPM97 B
AYCeLhqB…eqGM6KK1
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.923 Γ— 10⁹⁷(98-digit number)
19239049754713389995…18067433975328311839
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.923 Γ— 10⁹⁷(98-digit number)
19239049754713389995…18067433975328311839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.923 Γ— 10⁹⁷(98-digit number)
19239049754713389995…18067433975328311841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.847 Γ— 10⁹⁷(98-digit number)
38478099509426779991…36134867950656623679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.847 Γ— 10⁹⁷(98-digit number)
38478099509426779991…36134867950656623681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
7.695 Γ— 10⁹⁷(98-digit number)
76956199018853559983…72269735901313247359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.695 Γ— 10⁹⁷(98-digit number)
76956199018853559983…72269735901313247361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.539 Γ— 10⁹⁸(99-digit number)
15391239803770711996…44539471802626494719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.539 Γ— 10⁹⁸(99-digit number)
15391239803770711996…44539471802626494721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.078 Γ— 10⁹⁸(99-digit number)
30782479607541423993…89078943605252989439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.078 Γ— 10⁹⁸(99-digit number)
30782479607541423993…89078943605252989441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,619,032 XPMΒ·at block #6,796,876 Β· updates every 60s
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