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Block #206,535

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2013, 8:59:16 PM Β· Difficulty 9.9013 Β· 6,590,026 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
83cdc889ae986372e6e9ac37965919b902f4596910e5e1291a999d80f23cf294
View on Chainz β†—

Height

#206,535

Difficulty

9.901294

Transactions

2

Size

573 B

Version

2

Bits

09e6bb36

Nonce

2,258

Timestamp

10/12/2013, 8:59:16 PM

Confirmations

6,590,026

Mined by

⛏️ P2SHAHbLmpj36ZcwzqeuUFuDjYaQBLmX4rJTua

Merkle Root

2814dc242359d79f235ebca46319da671968ab805d66b1dbac16d50e89e74cb1
Transactions (2)
Coinbase1bdf789f33c009…b77888e1e76c7e
1 in β†’ 1 out10.2000 XPM110 B
AHbLmpj3…mX4rJTua
eae7c3df148224…b027a2a26c8263
2 in β†’ 2 out11.9600 XPM374 B
AaLSb9of…hv6YjCwXAWR3kwCJ…bxSndap6
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.

1.571 Γ— 10⁹³(94-digit number)
15718532039382947162…88360621730256935999
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
1.571 Γ— 10⁹³(94-digit number)
15718532039382947162…88360621730256935999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.571 Γ— 10⁹³(94-digit number)
15718532039382947162…88360621730256936001
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
3.143 Γ— 10⁹³(94-digit number)
31437064078765894325…76721243460513871999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.143 Γ— 10⁹³(94-digit number)
31437064078765894325…76721243460513872001
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
6.287 Γ— 10⁹³(94-digit number)
62874128157531788650…53442486921027743999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.287 Γ— 10⁹³(94-digit number)
62874128157531788650…53442486921027744001
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
1.257 Γ— 10⁹⁴(95-digit number)
12574825631506357730…06884973842055487999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.257 Γ— 10⁹⁴(95-digit number)
12574825631506357730…06884973842055488001
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
2.514 Γ— 10⁹⁴(95-digit number)
25149651263012715460…13769947684110975999
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:57,616,487 XPMΒ·at block #6,796,560 Β· updates every 60s
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