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Block #2,706,206

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/15/2018, 10:25:37 AM Β· Difficulty 11.6125 Β· 4,136,691 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2341c42732e49011be8bc897deba046226a5d871ba47afa31e3b99c17a081d1f
View on Chainz β†—

Height

#2,706,206

Difficulty

11.612515

Transactions

2

Size

689 B

Version

2

Bits

0b9ccdc3

Nonce

114,770,782

Timestamp

6/15/2018, 10:25:37 AM

Confirmations

4,136,691

Mined by

⛏️ P2SHAP75WGyqCn5CgGC8B6fXxsoRHNbnA6enSk

Merkle Root

08fbd9e8dcdb4a359cc4fded241df5ffcc9fb47f647a146ed3cd153fd5db4075
Transactions (2)
Coinbase22af1616227f79…59fc889d25555b
1 in β†’ 1 out7.4100 XPM110 B
AP75WGyq…bnA6enSk
428a99efe55ef2…3071fa0a33feb7
3 in β†’ 1 out11.9900 XPM489 B
ASVLgTSP…eFPhvU7R
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.

3.723 Γ— 10⁹⁡(96-digit number)
37237109460948753562…35294871801388584159
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
3.723 Γ— 10⁹⁡(96-digit number)
37237109460948753562…35294871801388584159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.723 Γ— 10⁹⁡(96-digit number)
37237109460948753562…35294871801388584161
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
7.447 Γ— 10⁹⁡(96-digit number)
74474218921897507124…70589743602777168319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.447 Γ— 10⁹⁡(96-digit number)
74474218921897507124…70589743602777168321
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
1.489 Γ— 10⁹⁢(97-digit number)
14894843784379501424…41179487205554336639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.489 Γ— 10⁹⁢(97-digit number)
14894843784379501424…41179487205554336641
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
2.978 Γ— 10⁹⁢(97-digit number)
29789687568759002849…82358974411108673279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.978 Γ— 10⁹⁢(97-digit number)
29789687568759002849…82358974411108673281
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
5.957 Γ— 10⁹⁢(97-digit number)
59579375137518005699…64717948822217346559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.957 Γ— 10⁹⁢(97-digit number)
59579375137518005699…64717948822217346561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.191 Γ— 10⁹⁷(98-digit number)
11915875027503601139…29435897644434693119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,987,524 XPMΒ·at block #6,842,896 Β· updates every 60s
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