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Block #212,427

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/16/2013, 6:56:40 AM Β· Difficulty 9.9189 Β· 6,604,882 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35a28b111591f0457afcf66b6182f80a0a692704b5d045feb6fe2a39af877df0
View on Chainz β†—

Height

#212,427

Difficulty

9.918935

Transactions

2

Size

574 B

Version

2

Bits

09eb3f54

Nonce

8,687

Timestamp

10/16/2013, 6:56:40 AM

Confirmations

6,604,882

Mined by

⛏️ P2SHANhBYN2SEW7rbkjcwTxrVMFUB1W53F3KTQ

Merkle Root

f775f6b27fb8de5b06639717fdf07e8d79a8b9ad384913cdb28fdc15ba5d743c
Transactions (2)
Coinbase18d687428c640b…2276d06ae5cfa7
1 in β†’ 1 out10.1600 XPM109 B
ANhBYN2S…W53F3KTQ
eac1b956c013bc…17c1f6c0b9cb4b
2 in β†’ 2 out77.2541 XPM374 B
Af3ZDREs…4mGdqDCPARhCbLRv…bBk9PrCh
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.

5.986 Γ— 10⁹⁢(97-digit number)
59862469633902751149…73944447340377115519
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
5.986 Γ— 10⁹⁢(97-digit number)
59862469633902751149…73944447340377115519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.986 Γ— 10⁹⁢(97-digit number)
59862469633902751149…73944447340377115521
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
1.197 Γ— 10⁹⁷(98-digit number)
11972493926780550229…47888894680754231039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.197 Γ— 10⁹⁷(98-digit number)
11972493926780550229…47888894680754231041
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
2.394 Γ— 10⁹⁷(98-digit number)
23944987853561100459…95777789361508462079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.394 Γ— 10⁹⁷(98-digit number)
23944987853561100459…95777789361508462081
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
4.788 Γ— 10⁹⁷(98-digit number)
47889975707122200919…91555578723016924159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.788 Γ— 10⁹⁷(98-digit number)
47889975707122200919…91555578723016924161
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
9.577 Γ— 10⁹⁷(98-digit number)
95779951414244401839…83111157446033848319
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:57,782,516 XPMΒ·at block #6,817,308 Β· updates every 60s
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