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Block #1,371,698

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 4:20:40 PM Β· Difficulty 10.8109 Β· 5,473,659 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c476cb34984fd19689fd4a8e498b66a708a46d92edd201728ad3608c075c327
View on Chainz β†—

Height

#1,371,698

Difficulty

10.810946

Transactions

1

Size

200 B

Version

2

Bits

0acf9a21

Nonce

928,960,013

Timestamp

12/16/2015, 4:20:40 PM

Confirmations

5,473,659

Mined by

⛏️ P2SHAX7Vevz8snCtb11Z7AmLgc7DcVWWNokv92

Merkle Root

299fee044484c136f153572679d5a8f068fcc0648208a54cf19bda392098186f
Transactions (1)
Coinbase299fee044484c1…9bda392098186f
1 in β†’ 1 out8.5400 XPM110 B
AX7Vevz8…WWNokv92
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.

9.196 Γ— 10⁹⁴(95-digit number)
91960536065993812102…34976271408526561599
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
9.196 Γ— 10⁹⁴(95-digit number)
91960536065993812102…34976271408526561599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.196 Γ— 10⁹⁴(95-digit number)
91960536065993812102…34976271408526561601
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
1.839 Γ— 10⁹⁡(96-digit number)
18392107213198762420…69952542817053123199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.839 Γ— 10⁹⁡(96-digit number)
18392107213198762420…69952542817053123201
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
3.678 Γ— 10⁹⁡(96-digit number)
36784214426397524841…39905085634106246399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.678 Γ— 10⁹⁡(96-digit number)
36784214426397524841…39905085634106246401
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
7.356 Γ— 10⁹⁡(96-digit number)
73568428852795049682…79810171268212492799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.356 Γ— 10⁹⁡(96-digit number)
73568428852795049682…79810171268212492801
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
1.471 Γ— 10⁹⁢(97-digit number)
14713685770559009936…59620342536424985599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.471 Γ— 10⁹⁢(97-digit number)
14713685770559009936…59620342536424985601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.942 Γ— 10⁹⁢(97-digit number)
29427371541118019872…19240685072849971199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,007,300 XPMΒ·at block #6,845,356 Β· updates every 60s
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