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Block #470,321

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/1/2014, 7:52:14 PM Β· Difficulty 10.4325 Β· 6,339,561 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d6937a76373c5b2e8fc78ea781f9fa7123f35c91a53370fc51ceb9439f2091c1
View on Chainz β†—

Height

#470,321

Difficulty

10.432482

Transactions

2

Size

418 B

Version

2

Bits

0a6eb724

Nonce

297,875

Timestamp

4/1/2014, 7:52:14 PM

Confirmations

6,339,561

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

dce3b9a1f5a6bde18fa4054ba0a190bae4f76a215524ca01d3b99f139581085f
Transactions (2)
Coinbaseb6043722f2fd0b…d632efd7f50219
1 in β†’ 1 out9.1800 XPM101 B
ASXb8Msj…BxGf64iZ
45ea92919a0fc9…8e5edcd0fadae2
1 in β†’ 2 out2.7869 XPM226 B
AKSgi7NT…e215W48RAaHaNnZZ…w5CtpS4F
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.

1.239 Γ— 10⁹⁢(97-digit number)
12397384767330622683…70240743964883979999
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
1.239 Γ— 10⁹⁢(97-digit number)
12397384767330622683…70240743964883979999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.239 Γ— 10⁹⁢(97-digit number)
12397384767330622683…70240743964883980001
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
2.479 Γ— 10⁹⁢(97-digit number)
24794769534661245367…40481487929767959999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.479 Γ— 10⁹⁢(97-digit number)
24794769534661245367…40481487929767960001
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
4.958 Γ— 10⁹⁢(97-digit number)
49589539069322490735…80962975859535919999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.958 Γ— 10⁹⁢(97-digit number)
49589539069322490735…80962975859535920001
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
9.917 Γ— 10⁹⁢(97-digit number)
99179078138644981470…61925951719071839999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.917 Γ— 10⁹⁢(97-digit number)
99179078138644981470…61925951719071840001
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
1.983 Γ— 10⁹⁷(98-digit number)
19835815627728996294…23851903438143679999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.983 Γ— 10⁹⁷(98-digit number)
19835815627728996294…23851903438143680001
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:57,723,143 XPMΒ·at block #6,809,881 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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