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Block #2,870,631

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/7/2018, 4:02:30 AM Β· Difficulty 11.6651 Β· 3,972,459 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e407ff3a307b3442f0fdf078637579e8239a48288149a428e4045d5929976464
View on Chainz β†—

Height

#2,870,631

Difficulty

11.665112

Transactions

1

Size

200 B

Version

2

Bits

0baa44c0

Nonce

1,561,287,898

Timestamp

10/7/2018, 4:02:30 AM

Confirmations

3,972,459

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

2ff300cec4b48701fd4683fca2748b26bb159d5e41beba962be42507d59334d1
Transactions (1)
Coinbase2ff300cec4b487…e42507d59334d1
1 in β†’ 1 out7.3400 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.419 Γ— 10⁹⁴(95-digit number)
34195479571398899637…03582483577281740799
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
3.419 Γ— 10⁹⁴(95-digit number)
34195479571398899637…03582483577281740799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.419 Γ— 10⁹⁴(95-digit number)
34195479571398899637…03582483577281740801
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
6.839 Γ— 10⁹⁴(95-digit number)
68390959142797799274…07164967154563481599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.839 Γ— 10⁹⁴(95-digit number)
68390959142797799274…07164967154563481601
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
1.367 Γ— 10⁹⁡(96-digit number)
13678191828559559854…14329934309126963199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.367 Γ— 10⁹⁡(96-digit number)
13678191828559559854…14329934309126963201
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
2.735 Γ— 10⁹⁡(96-digit number)
27356383657119119709…28659868618253926399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.735 Γ— 10⁹⁡(96-digit number)
27356383657119119709…28659868618253926401
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
5.471 Γ— 10⁹⁡(96-digit number)
54712767314238239419…57319737236507852799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.471 Γ— 10⁹⁡(96-digit number)
54712767314238239419…57319737236507852801
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
1.094 Γ— 10⁹⁢(97-digit number)
10942553462847647883…14639474473015705599
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:57,989,082 XPMΒ·at block #6,843,089 Β· updates every 60s
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