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Block #123,699

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/19/2013, 5:15:39 AM Β· Difficulty 9.7657 Β· 6,693,339 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5ebeb713502a08243ac27684bcafcf03a500058e7f7cc398c059421f0ae1a40f
View on Chainz β†—

Height

#123,699

Difficulty

9.765696

Transactions

1

Size

201 B

Version

2

Bits

09c404ac

Nonce

160,252

Timestamp

8/19/2013, 5:15:39 AM

Confirmations

6,693,339

Mined by

⛏️ P2SHASki8pmAYiSmpQcpe6L3Yu14B9Dwetzr7b

Merkle Root

b8b2b92baadc37b780cff98f39d620c754f90bb10447c3da4bd1f635a929e6c9
Transactions (1)
Coinbaseb8b2b92baadc37…d1f635a929e6c9
1 in β†’ 1 out10.4700 XPM109 B
ASki8pmA…Dwetzr7b
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.

1.086 Γ— 10¹⁰⁰(101-digit number)
10861861162966958592…20677092601367815499
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
1.086 Γ— 10¹⁰⁰(101-digit number)
10861861162966958592…20677092601367815499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.086 Γ— 10¹⁰⁰(101-digit number)
10861861162966958592…20677092601367815501
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
2.172 Γ— 10¹⁰⁰(101-digit number)
21723722325933917185…41354185202735630999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.172 Γ— 10¹⁰⁰(101-digit number)
21723722325933917185…41354185202735631001
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
4.344 Γ— 10¹⁰⁰(101-digit number)
43447444651867834371…82708370405471261999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.344 Γ— 10¹⁰⁰(101-digit number)
43447444651867834371…82708370405471262001
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
8.689 Γ— 10¹⁰⁰(101-digit number)
86894889303735668742…65416740810942523999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.689 Γ— 10¹⁰⁰(101-digit number)
86894889303735668742…65416740810942524001
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
1.737 Γ— 10¹⁰¹(102-digit number)
17378977860747133748…30833481621885047999
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:57,780,336 XPMΒ·at block #6,817,037 Β· updates every 60s
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