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Block #423,691

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/28/2014, 2:32:12 PM Β· Difficulty 10.3789 Β· 6,392,322 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d9aefafaeabb0097be48ae2f328f642a22f94ede3319b705bf88f89ca6c980f9
View on Chainz β†—

Height

#423,691

Difficulty

10.378864

Transactions

2

Size

721 B

Version

2

Bits

0a60fd38

Nonce

5,283,979

Timestamp

2/28/2014, 2:32:12 PM

Confirmations

6,392,322

Mined by

⛏️ P2SHAJ6exsAivrF78QZ6uqcugFECZxzz52qvLy

Merkle Root

0fa0f4b12e555548c375a7338de30e31c0d2ebc9bac678adc0ec3503fa03a1ef
Transactions (2)
Coinbasec6551ddfbabb6e…07fe97ced7afa6
1 in β†’ 1 out9.2800 XPM109 B
AJ6exsAi…zz52qvLy
9e0eea83d2e48d…000177c4a496d0
3 in β†’ 2 out3.1158 XPM522 B
AbGPF8Te…pgbKSb2bAaPPoJX2…LqYf17aE
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.

3.087 Γ— 10⁹⁴(95-digit number)
30875109419569881308…43292123739747415039
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
3.087 Γ— 10⁹⁴(95-digit number)
30875109419569881308…43292123739747415039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.087 Γ— 10⁹⁴(95-digit number)
30875109419569881308…43292123739747415041
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
6.175 Γ— 10⁹⁴(95-digit number)
61750218839139762617…86584247479494830079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.175 Γ— 10⁹⁴(95-digit number)
61750218839139762617…86584247479494830081
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
1.235 Γ— 10⁹⁡(96-digit number)
12350043767827952523…73168494958989660159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.235 Γ— 10⁹⁡(96-digit number)
12350043767827952523…73168494958989660161
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
2.470 Γ— 10⁹⁡(96-digit number)
24700087535655905047…46336989917979320319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.470 Γ— 10⁹⁡(96-digit number)
24700087535655905047…46336989917979320321
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
4.940 Γ— 10⁹⁡(96-digit number)
49400175071311810094…92673979835958640639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.940 Γ— 10⁹⁡(96-digit number)
49400175071311810094…92673979835958640641
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:57,772,222 XPMΒ·at block #6,816,012 Β· updates every 60s
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