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Block #1,241,398

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2015, 11:46:21 PM Β· Difficulty 10.7560 Β· 5,601,932 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
be8ad6dd6cc08b44be1b012a07d4016c1145d7b9c96749cc34047bcce54ffa8d
View on Chainz β†—

Height

#1,241,398

Difficulty

10.756013

Transactions

2

Size

2.15 KB

Version

2

Bits

0ac18a0d

Nonce

1,050,594,588

Timestamp

9/17/2015, 11:46:21 PM

Confirmations

5,601,932

Mined by

⛏️ P2SHAG8sWQv5y2Az697Kn5QrcmzqQXVNF1cbL8

Merkle Root

c0e605dc2589b5afae0c93051cd3da2b1c7531a2478b1f219d049e98377b1880
Transactions (2)
Coinbase4f10feb6026583…5bab324a731a1d
1 in β†’ 1 out8.6600 XPM109 B
AG8sWQv5…VNF1cbL8
510c8484fe00fd…5e9ee723400fc4
13 in β†’ 2 out129.0667 XPM1.96 KB
AQ8obrRF…hCezsXdrAQXx285Z…BRLzZaU2
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.

8.681 Γ— 10⁹⁴(95-digit number)
86816680335789000184…29355791701491411199
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
8.681 Γ— 10⁹⁴(95-digit number)
86816680335789000184…29355791701491411199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.681 Γ— 10⁹⁴(95-digit number)
86816680335789000184…29355791701491411201
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
1.736 Γ— 10⁹⁡(96-digit number)
17363336067157800036…58711583402982822399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.736 Γ— 10⁹⁡(96-digit number)
17363336067157800036…58711583402982822401
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
3.472 Γ— 10⁹⁡(96-digit number)
34726672134315600073…17423166805965644799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.472 Γ— 10⁹⁡(96-digit number)
34726672134315600073…17423166805965644801
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
6.945 Γ— 10⁹⁡(96-digit number)
69453344268631200147…34846333611931289599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.945 Γ— 10⁹⁡(96-digit number)
69453344268631200147…34846333611931289601
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
1.389 Γ— 10⁹⁢(97-digit number)
13890668853726240029…69692667223862579199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.389 Γ— 10⁹⁢(97-digit number)
13890668853726240029…69692667223862579201
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:57,991,001 XPMΒ·at block #6,843,329 Β· updates every 60s
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