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Block #210,777

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 8:47:21 AM Β· Difficulty 9.9135 Β· 6,607,089 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e7d4b661d813db0699b158f93ddf5b19e40c2bd9f42ff5c7d7bcab99fc597d5c
View on Chainz β†—

Height

#210,777

Difficulty

9.913505

Transactions

1

Size

205 B

Version

2

Bits

09e9db70

Nonce

1,733

Timestamp

10/15/2013, 8:47:21 AM

Confirmations

6,607,089

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

b7c9a4866e0bde67fcc5795cc985a4ae2a2f5081fe52e75cb90c1b30f47a1b8e
Transactions (1)
Coinbaseb7c9a4866e0bde…0c1b30f47a1b8e
1 in β†’ 1 out10.1600 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.699 Γ— 10⁹³(94-digit number)
26994031317367382269…69240236929610982399
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
2.699 Γ— 10⁹³(94-digit number)
26994031317367382269…69240236929610982399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.699 Γ— 10⁹³(94-digit number)
26994031317367382269…69240236929610982401
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
5.398 Γ— 10⁹³(94-digit number)
53988062634734764538…38480473859221964799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.398 Γ— 10⁹³(94-digit number)
53988062634734764538…38480473859221964801
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
1.079 Γ— 10⁹⁴(95-digit number)
10797612526946952907…76960947718443929599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.079 Γ— 10⁹⁴(95-digit number)
10797612526946952907…76960947718443929601
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
2.159 Γ— 10⁹⁴(95-digit number)
21595225053893905815…53921895436887859199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.159 Γ— 10⁹⁴(95-digit number)
21595225053893905815…53921895436887859201
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
4.319 Γ— 10⁹⁴(95-digit number)
43190450107787811630…07843790873775718399
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:57,786,995 XPMΒ·at block #6,817,865 Β· updates every 60s
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