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Block #1,407,263

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2016, 11:49:26 AM Β· Difficulty 10.8059 Β· 5,410,763 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
11654b63111963440be057e105fccbfca588c40039093eb38ca02a634834dd2c
View on Chainz β†—

Height

#1,407,263

Difficulty

10.805918

Transactions

2

Size

6.35 KB

Version

2

Bits

0ace50a2

Nonce

651,420,129

Timestamp

1/10/2016, 11:49:26 AM

Confirmations

5,410,763

Mined by

⛏️ P2SHAbKchAomaaVwCoqjxu4rTcZQZ1Rok7Na2p

Merkle Root

5b6e579e71954667fe4274e72b2918a41878d5f40b3db613417952756cb31602
Transactions (2)
Coinbase2f8108f61f5439…eaa4bfb639b437
1 in β†’ 1 out8.6300 XPM110 B
AbKchAom…Rok7Na2p
4671e64b01cd2e…002d56469eb506
42 in β†’ 2 out32.7622 XPM6.15 KB
AbhmmiyP…6qxLyCXuAGky5ni4…jnaoQ88P
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.

4.004 Γ— 10⁹⁴(95-digit number)
40048418412999330175…61264013501728038399
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
4.004 Γ— 10⁹⁴(95-digit number)
40048418412999330175…61264013501728038399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.004 Γ— 10⁹⁴(95-digit number)
40048418412999330175…61264013501728038401
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
8.009 Γ— 10⁹⁴(95-digit number)
80096836825998660351…22528027003456076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.009 Γ— 10⁹⁴(95-digit number)
80096836825998660351…22528027003456076801
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
1.601 Γ— 10⁹⁡(96-digit number)
16019367365199732070…45056054006912153599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.601 Γ— 10⁹⁡(96-digit number)
16019367365199732070…45056054006912153601
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
3.203 Γ— 10⁹⁡(96-digit number)
32038734730399464140…90112108013824307199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.203 Γ— 10⁹⁡(96-digit number)
32038734730399464140…90112108013824307201
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
6.407 Γ— 10⁹⁡(96-digit number)
64077469460798928280…80224216027648614399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.407 Γ— 10⁹⁡(96-digit number)
64077469460798928280…80224216027648614401
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:57,788,276 XPMΒ·at block #6,818,025 Β· updates every 60s
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