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Block #420,380

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/26/2014, 8:24:28 AM Β· Difficulty 10.3702 Β· 6,394,475 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bb479f358a5fd49402d5064a46f831de1c48f7bc293731d6a4ccae37d2dcbde0
View on Chainz β†—

Height

#420,380

Difficulty

10.370175

Transactions

2

Size

539 B

Version

2

Bits

0a5ec3d2

Nonce

17,440,651

Timestamp

2/26/2014, 8:24:28 AM

Confirmations

6,394,475

Mined by

⛏️ P2SHASETynLBYWQn4P27HzSYpaboFJ7aVXhwcx

Merkle Root

63186329c9034594a1c6defd38727a1cd76c3537b76ea7167942c60a18fbf2b6
Transactions (2)
Coinbasec7bd516b852e6f…15bc13d838a9fb
1 in β†’ 1 out9.2900 XPM109 B
ASETynLB…7aVXhwcx
81d440b7ca30b3…9aeb26b9bc6555
2 in β†’ 1 out6.0089 XPM340 B
AGKj1VZw…bhwpBHGN
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.

7.997 Γ— 10⁹⁡(96-digit number)
79974108670782213431…91245260001267071999
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
7.997 Γ— 10⁹⁡(96-digit number)
79974108670782213431…91245260001267071999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.997 Γ— 10⁹⁡(96-digit number)
79974108670782213431…91245260001267072001
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
1.599 Γ— 10⁹⁢(97-digit number)
15994821734156442686…82490520002534143999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.599 Γ— 10⁹⁢(97-digit number)
15994821734156442686…82490520002534144001
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
3.198 Γ— 10⁹⁢(97-digit number)
31989643468312885372…64981040005068287999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.198 Γ— 10⁹⁢(97-digit number)
31989643468312885372…64981040005068288001
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
6.397 Γ— 10⁹⁢(97-digit number)
63979286936625770745…29962080010136575999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.397 Γ— 10⁹⁢(97-digit number)
63979286936625770745…29962080010136576001
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
1.279 Γ— 10⁹⁷(98-digit number)
12795857387325154149…59924160020273151999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.279 Γ— 10⁹⁷(98-digit number)
12795857387325154149…59924160020273152001
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:57,762,923 XPMΒ·at block #6,814,854 Β· updates every 60s
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