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Block #2,121,522

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/18/2017, 1:51:27 AM Β· Difficulty 10.9136 Β· 4,715,199 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d4eca354586058a80fb2786a1881ccbed6869b6f75f95b0098452fc903f3fa48
View on Chainz β†—

Height

#2,121,522

Difficulty

10.913562

Transactions

1

Size

199 B

Version

2

Bits

0ae9df32

Nonce

504,175,788

Timestamp

5/18/2017, 1:51:27 AM

Confirmations

4,715,199

Mined by

⛏️ P2SHAbs9BALYK7mZsM2toYAyuvCsfib3fx41DP

Merkle Root

926833fc52bb6f5daae7e43e42e9f0e7cec89a205479e5a4d240027d0cee15b7
Transactions (1)
Coinbase926833fc52bb6f…40027d0cee15b7
1 in β†’ 1 out8.3800 XPM109 B
Abs9BALY…b3fx41DP
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.

2.035 Γ— 10⁹⁡(96-digit number)
20357373005686567265…18564062085808297599
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
2.035 Γ— 10⁹⁡(96-digit number)
20357373005686567265…18564062085808297599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.035 Γ— 10⁹⁡(96-digit number)
20357373005686567265…18564062085808297601
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
4.071 Γ— 10⁹⁡(96-digit number)
40714746011373134530…37128124171616595199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.071 Γ— 10⁹⁡(96-digit number)
40714746011373134530…37128124171616595201
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
8.142 Γ— 10⁹⁡(96-digit number)
81429492022746269061…74256248343233190399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.142 Γ— 10⁹⁡(96-digit number)
81429492022746269061…74256248343233190401
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
1.628 Γ— 10⁹⁢(97-digit number)
16285898404549253812…48512496686466380799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.628 Γ— 10⁹⁢(97-digit number)
16285898404549253812…48512496686466380801
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
3.257 Γ— 10⁹⁢(97-digit number)
32571796809098507624…97024993372932761599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.257 Γ— 10⁹⁢(97-digit number)
32571796809098507624…97024993372932761601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,938,050 XPMΒ·at block #6,836,720 Β· updates every 60s
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