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Block #206,360

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2013, 6:21:14 PM Β· Difficulty 9.9010 Β· 6,602,975 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c5de8f5368aaa9be58766b9c6f9e597c53e05e7b6ab20afabcf191e4330aff36
View on Chainz β†—

Height

#206,360

Difficulty

9.900964

Transactions

1

Size

198 B

Version

2

Bits

09e6a59a

Nonce

79,925

Timestamp

10/12/2013, 6:21:14 PM

Confirmations

6,602,975

Mined by

⛏️ P2SHASHCgr3FcMvAMVeUbxmte178wGe7VPFbY8

Merkle Root

d269dee893365cdb82b8ef23c4dd4e992af5a8d5b98cd3471c2c3d1bc9726a3c
Transactions (1)
Coinbased269dee893365c…2c3d1bc9726a3c
1 in β†’ 1 out10.1900 XPM109 B
ASHCgr3F…e7VPFbY8
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— 10⁹³(94-digit number)
34198025975303773611…17731939046648890199
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— 10⁹³(94-digit number)
34198025975303773611…17731939046648890199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.419 Γ— 10⁹³(94-digit number)
34198025975303773611…17731939046648890201
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— 10⁹³(94-digit number)
68396051950607547222…35463878093297780399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.839 Γ— 10⁹³(94-digit number)
68396051950607547222…35463878093297780401
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— 10⁹⁴(95-digit number)
13679210390121509444…70927756186595560799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.367 Γ— 10⁹⁴(95-digit number)
13679210390121509444…70927756186595560801
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— 10⁹⁴(95-digit number)
27358420780243018888…41855512373191121599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.735 Γ— 10⁹⁴(95-digit number)
27358420780243018888…41855512373191121601
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— 10⁹⁴(95-digit number)
54716841560486037777…83711024746382243199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,718,747 XPMΒ·at block #6,809,334 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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