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Block #1,102,803

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/13/2015, 3:08:36 PM Β· Difficulty 10.7529 Β· 5,703,483 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c203a0cb07b7113ea9e577eb7a31aa39ff0e8deb972020d144754872ff8f2151
View on Chainz β†—

Height

#1,102,803

Difficulty

10.752907

Transactions

2

Size

1.86 KB

Version

2

Bits

0ac0be86

Nonce

1,945,048,529

Timestamp

6/13/2015, 3:08:36 PM

Confirmations

5,703,483

Mined by

⛏️ P2SHAX6zbjSeKNo5pUs8aucENc3jj662p5de3Y

Merkle Root

08019d9e972eb480a43e43227a07e278582dfa0f7eacb173181201d15a987781
Transactions (2)
Coinbase0af521440b493c…ea0f5c142b2341
1 in β†’ 1 out8.6600 XPM109 B
AX6zbjSe…62p5de3Y
696058ee5aa776…ef0366d097c08f
11 in β†’ 2 out2000.0111 XPM1.67 KB
ATNnn9ok…6UTPaJtmAXjLMbPs…jw2JP1yY
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.

1.815 Γ— 10⁹⁢(97-digit number)
18156281510944018772…61443886483361251839
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
1.815 Γ— 10⁹⁢(97-digit number)
18156281510944018772…61443886483361251839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.815 Γ— 10⁹⁢(97-digit number)
18156281510944018772…61443886483361251841
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
3.631 Γ— 10⁹⁢(97-digit number)
36312563021888037545…22887772966722503679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.631 Γ— 10⁹⁢(97-digit number)
36312563021888037545…22887772966722503681
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
7.262 Γ— 10⁹⁢(97-digit number)
72625126043776075091…45775545933445007359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.262 Γ— 10⁹⁢(97-digit number)
72625126043776075091…45775545933445007361
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
1.452 Γ— 10⁹⁷(98-digit number)
14525025208755215018…91551091866890014719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.452 Γ— 10⁹⁷(98-digit number)
14525025208755215018…91551091866890014721
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
2.905 Γ— 10⁹⁷(98-digit number)
29050050417510430036…83102183733780029439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.905 Γ— 10⁹⁷(98-digit number)
29050050417510430036…83102183733780029441
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:57,694,374 XPMΒ·at block #6,806,285 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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